Career summary

Details for Mathematicians


Description

Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve or direct solutions to problems in various fields by mathematical methods.

Tasks

  • Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
  • Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
  • Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
  • Assemble sets of assumptions and explore the consequences of each set.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  • Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  • Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  • Perform computations and apply methods of numerical analysis to data.
  • Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
  • Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
  • Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.

Interests

  • Investigative - Investigative occupations frequently involve working with ideas, and require an extensive amount of thinking. These occupations can involve searching for facts and figuring out problems mentally.
  • Artistic - Artistic occupations frequently involve working with forms, designs and patterns. They often require self-expression and the work can be done without following a clear set of rules.
  • Conventional - Conventional occupations frequently involve following set procedures and routines. These occupations can include working with data and details more than with ideas. Usually there is a clear line of authority to follow.

Education, training, experience

  • Education - Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
  • Training - Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
  • Experience - Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.

Knowledge

  • Customer and Personal Service - Knowledge of principles and processes for providing customer and personal services. This includes customer needs assessment, meeting quality standards for services, and evaluation of customer satisfaction.
  • Administration and Management - Knowledge of business and management principles involved in strategic planning, resource allocation, human resources modeling, leadership technique, production methods, and coordination of people and resources.
  • Education and Training - Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
  • Physics - Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.
  • Engineering and Technology - Knowledge of the practical application of engineering science and technology. This includes applying principles, techniques, procedures, and equipment to the design and production of various goods and services.
  • English Language - Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
  • Computers and Electronics - Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
  • Mathematics - Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.

Skills

  • Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
  • Active Listening - Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
  • Writing - Communicating effectively in writing as appropriate for the needs of the audience.
  • Speaking - Talking to others to convey information effectively.
  • Mathematics - Using mathematics to solve problems.
  • Science - Using scientific rules and methods to solve problems.
  • Critical Thinking - Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
  • Active Learning - Understanding the implications of new information for both current and future problem-solving and decision-making.
  • Learning Strategies - Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
  • Instructing - Teaching others how to do something.
  • Complex Problem Solving - Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
  • Judgment and Decision Making - Considering the relative costs and benefits of potential actions to choose the most appropriate one.
  • Systems Analysis - Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.

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